傅立叶展开法测相位的误差分析

Error Analysis of Phase Measurement Using Fourier Transform

应用离散傅立叶变换法测量正弦信号相位差可以克服时间间隔测量法对随机噪声、谐波失真和零点漂移等比较敏感的弱点,但是采用离散傅立叶变换法测量相位差时,存在相位测量不确定度与测试信号信噪比、量化精度、采样点数和测量时间的优化问题。在简单介绍用离散傅立叶变换(DFT)法测量正弦信号相位的基本原理和实现方法的基础上,重点分析了测试信号信噪比与相位测量不确定度的关系,得出了测试信号的相位测量不确定度与DFT变换后测试信号的信噪比成反比的结论。同时给出了提高测试信号的信噪比可以通过减小噪声总能量、增加采样点数、提高测试信号的幅度等来实现。最后对分析结果进行了仿真验证,仿真结果与理论分析结果一致。在IPD测试仪设计中,以上述结论为依据进行设计,实际测量结果与理论分析比较吻合。

Using DFT for phase measurement can overcome the disadvantage of being sensible to random noise, harmonic distortion and zero excursions, but this method have to optimize between measurement uncertainty and SNR of the signal to be tested, digitizing precision, number of samples as well as measurement time. After introducing the basic principle of using DFT in sinusoidal signal phase measurement, the relationship between SNR of the signal to be tested and uncertainty of phase measurement is analyzed emphatically. The conclusion is derived, that is the uncertainty of phase measurement is inversely proportional to the SNR of the signal to be tested after DFT operation. To improve the SNR of the signal to be tested it is possible to reduce the total noise power, increase the number of samples and increase the amplitude of the signal to be tested. Computer simulation shows that the simulation result is consistent with the result of theoretic analysis. Based on above conclusion, an IPD measurement instrument was designed. Experiment result is consistent with the result of theoretic analysis.